Curve Modifier - not smooth enough deformation
You can try both method

Method 1

Select the curve go to curve tab and in Resolution - Preview U : increase from 12



Method 2

You have added loop cut vertically and no loop cut horizontally

So just select all and delete with limited dissolve

Press W key and add subdivide and Press f6 to increase the count to above 7

No need of subsurf modifier

Apply smooth shading.